Flux Coordinates and Magnetic Field Structure

Abstract

2nd rev. ed. Examples of stiff equations -- Stability analysis for explicit RK methods -- Stability function of implicit RK-methods -- Order stars -- Construction of implicit Runge-Kutta methods -- Diagonally implicit RK methods -- Rosenbrock-type methods -- Implementation of implicit Runge-Kutta methods -- Extrapolation methods -- Numerical experiments -- Contractivity for linear problems -- B-stability and Contractivity -- Positive quadrature formulas and B-stable RK-methods -- Existence and uniqueness of IRK solutions -- B-convergence -- Stability of multistep methods -- "Nearly" A-stable multistep methods -- Generalized multistep methods -- Order stars on Riemann surfaces -- Experiments with multistep codes -- One-leg methods and G-stability -- Convergence for linear problems -- Convergence for nonlinear problems -- Algebraic stability of general linear methods -- Solving index 1 problems -- Multistep methods -- Epsilon expansions for exact and RK solutions -- Rosenbrock methods -- Extrapolation methods -- Quasilinear problems -- The index and various examples -- Index reduction methods -- Multistep methods for index 2 DAE -- Runge-Kutta methods for index 2 DAE -- Order conditions for index 2 DAE -- Half-explicit methods for index 2 systems -- Computation of multibody mechanisms -- Symplectic methods for constrained Hamiltonian systems.